This invention relates in general to the determination of velocity as defined by the cosmic background Doppler shift by measuring the Reichenbach clock synchronization coefficients and the resulting vector velocity of light in the oscillations of photon tunneling times.
Einstein first introduced the idea of an ultimate particle speed known as c, the speed of light, with the publication of his special theory of relativity in 1905. Since this publication, scientists have shown that c is not an upper-limit on a particle's speed, but a barrier to acceleration. These mathematical studies have shown that while it is not possible to accelerate an object to a velocity faster than light, it is possible for an object to have a velocity greater than c.
In mathematical terms the one-way vacuum velocity of light from A to B is c(AB), which is described by the equation:c(AB)=c/2ε(AB)  (1)where ε(AB) are the Reichenbach clock synchronization coefficients. The vector velocity c(AB) is only isotropic in a preferred reference frame and the round trip vacuum speed of light, c, is constant because:ε(AB)=1−ε(BA)  (2)In the Lorentz covariant theoretical work, without “superluminal” energy flow, any inertial frame can be chosen as the preferred frame. Only by using “superluminal” energy flow, then, can a single preferred reference frame be used to measure the vector vacuum velocity of light.
The first evidence of energy moving at velocities greater than c was observed by radio engineers at the turn of the century. They learned that radio signals in the upper atmosphere traveled faster than light. The reason was that the radio waves were moving through ionized gas and not normal air. In effect, these radio waves' pulses have two different velocities, a group velocity, or the velocity of the pulse packet, and a phase velocity, the velocity of the individual waves within the group. In this example, the phase velocity of the radio waves, or the internal velocity of the individual waves within the radio wave pulse packet were moving faster than light. A more complete discussion of these early “superluminal” radio wave experiments can be found in the text Faster Than Light, by Nick Herbert, pg. 56–58, (1988).
Systems designed to transmit energy at “superluminal” velocities are also well-known in the art of quantum mechanics. One type of conventional “superluminal” energy transport method employs the phenomenon known as quantum barrier penetration, or tunneling. Under quantum theory, a quantum particle can be thought of as a wave packet, its width in space related to its velocity through the Heisenberg Uncertainty Relation. A common interpretation of this wave packet is that it represents a probability distribution. This means that where the amplitude of the wave packet is the greatest corresponds to the position in space with the highest probability of finding, or measuring, the particle. When the quantum wave packet is incident upon a barrier, it is partially reflected off the barrier and partially transmitted through the barrier. Since the packet transmitted through the barrier is a portion of the original probability distribution there is a small but finite probability of measuring the location of the quantum particle on the far side of the barrier. This phenomenon is known as tunneling and is well-known and accepted. However, a question arises as to the time required for the particle to achieve barrier penetration.
Several groups studying the phenomena of tunneling have shown that the tunneling velocities, or interaction times, for a variety of particles to pass through a barrier exceed c. For example, “superluminal” velocities have been measured for light pulses traveling through an absorbing material. “Superluminal” velocities have also been measured for the propagation for microwaves through a “forbidden zone” inside square metal waveguides. For a more detailed discussion of these experiments see, NEW SCIENTIST, vol. 146, pg. 27 (1995).
More recently, a group at the University of California at Berkeley measured “superluminal” tunneling times for visible light tunneling through a dielectric mirror using a Hong-Ou-Mandel interferometer. Similar experiments by a group in the University of Vienna in 1994 confirmed the Berkeley study and also showed that “superluminal” tunneling times could be obtained for increasingly large barrier thicknesses. For a more detailed discussion of these experiments see, NEW SCIENTIST, vol. 146, pg. 29 (1995).
Finally, in 1995, a group headed by Prof. Nimtz sent a microwave signal broadcasting Mozart's 40th Symphony across 12 cm of space at 4.7 times the speed of light. For a more detailed discussion of this experiment see, NEW SCIENTIST, vol. 146, pg. 30 (1995).
In effect, these experiments show that tunnel times are independent of tunnel length, demonstrating the Hartman effect and tunneling. Under this regime the tunneling time, At, is a saturated value and the Heisenberg uncertainty principle is written as follows:ΔτΔE=(1+O)/2  (3)where, , is the Heisenberg constant and, O, represent the higher order corrections to the tunneling time. This principle is referred to as the “energy borrowing” uncertainty principle, where the energy ΔE, must be “paid back” in a time less that Δt, regardless of the energy flow speed or group velocity required to do so. A more detailed explanation of the physics of tunneling is provided in the following references, each incorporated herein by reference: R. Y. Chiao, “Tunneling Times and Superluminality: a Tutorial”, quant-ph/9811019, 7 Nov. 1998, at LANL; J. Jakiel et al., “On Superluminal Motions in Photon and Particle Tunnelings”, quant-ph/9810053, 16 Oct. 1998, at LANL; A. Kempf, “A generalized Shannon Sampling Theorem, Fields at the Plank Scale as Bandlimited Signals”, hep-th/9905114, 2 Mar. 2000, at LANL; P. Bamberg and S. Sternberg, “A course in Mathematics for Students of Physics 2”, Cambridge University Press 1990, Sect. 21.4; J. Rembielinski, “Superluminal Phenomena and the Quantum Preferred Frame”, quant-ph/0010026, 6 Oct. 2000, at LANL; J. Rancourt, “Optical Thin Films User Handbook”, SPIE Optical Engineering Press, 1996, Apendix C; Hawking & Ellis, “The Large Scale Structure of Space-Time”, Cambridge University Press, 1973, Sect. 4.3.
While these experiments and texts clearly show the possibility of transmitting various forms of electromagnetic radiation faster than the speed of light, thus far no system has been developed to determine the one-way velocity vector of light utilizing these “superluminal” energy transmissions.